A collection of 28 refereed papers grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. Suitable for researchers, practitioners and postgrads.

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Extremum-seeking control tracks a varying maximum or minimum in a performance function such as output or cost. It attempts to determine the optimal performance of a control system as it operates, thereby reducing downtime and the need for system analysis. Extremum-seeking Control and Applications is divided into two parts. In the first, the authors review existing analog-optimization-based extremum-seeking control including gradient-, perturbation- and sliding-mode-based control designs. They then propose a novel numerical-optimization-based extremum-seeking control based on optimization algorithms and state regulation. This control design is developed for simple linear time-invariant systems and then extended for a class of feedback linearizable nonlinear systems. The two main optimization algorithms – line search and trust region methods – are analyzed for robustness. Finite-time and asymptotic state regulators are put forward for linear and nonlinear systems respectively. Further design flexibility is achieved using the robustness results of the optimization algorithms and the asymptotic state regulator by which existing nonlinear adaptive control techniques can be introduced for robust design. The approach used is easier to implement and tends to be more robust than those that use perturbation-based extremum-seeking control. The second part of the book deals with a variety of applications of extremum-seeking control: a comparative study of extremum-seeking control schemes in antilock braking system design; source seeking, formation control, collision and obstacle avoidance for groups of autonomous agents; mobile radar networks; and impedance matching. MATLAB®/Simulink® code which can be downloaded from www.springer.com/ISBN helps readers to reproduce the results presented in the text and gives them a head start for implementing the algorithms in their own applications. Extremum-seeking Control and Applications will interest academics and graduate students working in control, and industrial practitioners from a variety of backgrounds: systems, automotive, aerospace, communications, semiconductor and chemical engineering.

This book presents recent advances in optimization and control methods with applications to industrial engineering and construction management. It consists of 15 chapters authored by recognized experts in a variety of fields including control and operation research, industrial engineering and project management. Topics include numerical methods in unconstrained optimization, robust optimal control problems, set splitting problems, optimum confidence interval analysis, a monitoring networks optimization survey, distributed fault detection, nonferrous industrial optimization approaches, neural networks in traffic flows, economic scheduling of CCHP systems, a project scheduling optimization survey, lean and agile construction project management, practical construction projects in Hong Kong, dynamic project management, production control in PC4P and target contracts optimization. The book offers a valuable reference work for scientists, engineers, researchers and practitioners in industrial engineering and construction management.

A compendium of the authors’ recently published results, this book discusses sliding mode control of uncertain nonlinear systems, with a particular emphasis on advanced and optimization based algorithms. The authors survey classical sliding mode control theory and introduce four new methods of advanced sliding mode control. They analyze classical theory and advanced algorithms, with numerical results complementing the theoretical treatment. Case studies examine applications of the algorithms to complex robotics and power grid problems. Advanced and Optimization Based Sliding Mode Control: Theory and Applications is the first book to systematize the theory of optimization based higher order sliding mode control and illustrate advanced algorithms and their applications to real problems. It presents systematic treatment of event-triggered and model based event-triggered sliding mode control schemes, including schemes in combination with model predictive control, and presents adaptive algorithms as well as algorithms capable of dealing with state and input constraints. Additionally, the book includes simulations and experimental results obtained by applying the presented control strategies to real complex systems. This book is suitable for students and researchers interested in control theory. It will also be attractive to practitioners interested in implementing the illustrated strategies. It is accessible to anyone with a basic knowledge of control engineering, process physics, and applied mathematics.

Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.

The published material represents the outgrowth of teaching analytical optimization to aerospace engineering graduate students. To make the material available to the widest audience, the prerequisites are limited to calculus and differential equations. It is also a book about the mathematical aspects of optimal control theory. It was developed in an engineering environment from material learned by the author while applying it to the solution of engineering problems. One goal of the book is to help engineering graduate students learn the fundamentals which are needed to apply the methods to engineering problems. The examples are from geometry and elementary dynamical systems so that they can be understood by all engineering students. Another goal of this text is to unify optimization by using the differential of calculus to create the Taylor series expansions needed to derive the optimality conditions of optimal control theory.

This book offers a comprehensive presentation of optimization and polyoptimization methods. The examples included are taken from various domains: mechanics, electrical engineering, economy, informatics, and automatic control, making the book especially attractive. With the motto “from general abstraction to practical examples,” it presents the theory and applications of optimization step by step, from the function of one variable and functions of many variables with constraints, to infinite dimensional problems (calculus of variations), a continuation of which are optimization methods of dynamical systems, that is, dynamic programming and the maximum principle, and finishing with polyoptimization methods. It includes numerous practical examples, e.g., optimization of hierarchical systems, optimization of time-delay systems, rocket stabilization modeled by balancing a stick on a finger, a simplified version of the journey to the moon, optimization of hybrid systems and of the electrical long transmission line, analytical determination of extremal errors in dynamical systems of the rth order, multicriteria optimization with safety margins (the skeleton method), and ending with a dynamic model of bicycle. The book is aimed at readers who wish to study modern optimization methods, from problem formulation and proofs to practical applications illustrated by inspiring concrete examples.

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.